Question

The value of $\text{'}g\text{'}$ on the top of Mount Everest (height $8848m$) will be:

[Take radius of earth $6400000m$ and $g_{earth}=9.8m{s}^{-2}$]

• A. $9.77m{s}^{-2}$
• B. $6.77m{s}^{-2}$
• C. $6.67m{s}^{-2}$
• D. $5.77m{s}^{-2}$

Answer 1

The correct option is A

$9.77m{s}^{-2}$

Step 1: Given data

Height, $h=8848m$

Acceleration due to gravity, $g_{earth}=9.8m{s}^{-2}$

Radius of Earth, $R=6400000m$

Step 2: Calculating acceleration due to gravity

So, Let $g\prime$be the acceleration due to the gravity on the Mount Everest.

$g\prime =g(1-\frac{2h}{R})$

$\Rightarrow g\text{'}=9.8(1-\frac{17696}{6400000})$

$$\begin{gathered} \Rightarrow g\text{'}=9.8(1-0.00276) \\ \Rightarrow g\text{'}=9.8\times 0.99724 \\ \Rightarrow g\text{'}=9.773m{s}^{-2} \end{gathered}$$

Thus, the acceleration due to gravity on the top of Mount Everest is $9.773m{s}^{-2}$.

Hence, the correct answer is option (A) i.e. $9.773m{s}^{-2}$.